The dynamical problem for the TLS coupled to the reservoir with continuous spectrum has been investigated already in details
(see, e.g., review paper [1]}, monograph [2]}, or our publication [3]}).
The specific feature of this model is the transition from coherent oscillations between the initial and final state to exponential decay of the initial state population when the transition matrix element between the TLS states becomes smaller than the matrix element for the TLS-reservoir coupling. In this subsection, we investigate the problem for the case of the intra-molecular reservoir with the
equidistant spectrum (the bare Zwanzig model reservoirs).
The time dependent wave function of the TLS coupled to the reservoirs is described by a column with 2 terms which are the wave functions of the initial and final configurations coupled to the reservoirs
\(\Psi (t) = \left(\begin{array}{c}\Psi _L(t) \\\Psi _R(t)\end{array}\right)\, .\) 
